title: Generalized stochastic compartmental models with Erlang transit times.
abstract: This paper considers the use of semi-Markov process models with Erlang transit times for the description of compartmental systems. The semi-Markov models seem particularly useful for systems with nonhomogeneous "poorly-stirred" compartments. The paper reviews the Markov process models with exponential transit times, and illustrates the application of such models, describing the clearance of calcium in man. The semi-Markov model with Erlang transit times is then developed, and the solutions for its concentration-time curves and residence time moments are given. The use of semi-Markov models is illustrated with the same calcium data, and the results from the two models are compared. The example demonstrates that these semi-Markov models are physiologically more realistic than standard models and may be fitted to pharmacokinetic data using readily available software.
authors.affiliation: Department of Statistics, Texas A & M University, College Station 77843.
authors.forename: J H
authors.initials: JH
authors.lastname: Matis
authors.forename: T E
authors.initials: TE
authors.lastname: Wehrly
mesh_terms: D008433:Mathematics; D008954:Models, Biological; D010599:Pharmacokinetics